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3 years ago

A team won 9 of its first 12 games. At that rate, how many games will the team win if it plays 64 games in all?

Mathematics

2 answers:

FinnZ [79.3K]3 years ago

7 0

At that rate, if the team plays 64 games in all they will win 48 games.

Feliz [49]3 years ago

3 0

9 out of 12 = 9/12 which can be simplified to 3/4. So the team wins 3/4 of its games. 3/4 of 64 = 64 divided by 4 = 16. 16 x 3 = 48.

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2 years ago

Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).

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$\cos{\theta} = \dfrac{1}{52}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

$\sec{\theta} = \dfrac{1}{\cos{\theta}}$

we can substitute the value of sec(θ) in this equation:

$52 = \dfrac{1}{\cos{\theta}}$

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b) since right triangle is mentioned in the question. We can use:

$\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}$

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

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we can find the third side using the Pythagoras theorem.

$(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2$

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$\text{opp}=\sqrt{(52)^2-1}$

$\text{opp}=\sqrt{2703}$

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we can find the sin(θ) using this side:

$\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}$

$\sin{\theta} = \dfrac{\sqrt{2703}}{52}}$

and since $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

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3 years ago

2. A man buys eggs at 55kobo a score . he finds that 10% of the eggs are unsellable but sells the rest at 60kobo a dozen .find i

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Answer:

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The man buys 440 eggs at 55 pence a score

i.e. he buys 20 eggs for 55 pence

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Therefore, he buys 440 eggs for = 440 × 2.75 = 1210 pence

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thus he sold = 440 - 440 × 10/100 = 440 - 44 = 396 eggs

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Thus, he sold 33 dozen for = 33 × 60 = 1980 pence

Profit = 1980 - 1210 = 770 pence

% Profit = (770/1210) × 100 = 63.63%

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